Business-cycle Volatility and Long-run Growth: How Strong is the Relationship?*

Debdulal Mallick

Department of Economics, and Alfred Deakin Research Institute Deakin University

70 Elgar Road Burwood, VIC 3125, Australia Email: dmallic@deakin.edu.au

October 2014

* The author would like to thank Robert Chirinko, Lant Pritchett and participants at the 10th Australasian Development Economics Workshop and 2014 Australasian Econometric Society Meeting. All errors and omissions are the sole responsibility of the author.

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Business-cycle Volatility and Long-run Growth: How Strong is the Relationship?

Abstract

This paper revisits the empirical relationship between business-cycle volatility and long-run

growth. The key contribution lies in controlling for fluctuations in the trend growth that also

accounts for enormous heterogeneity among countries in their long-run growth trajectories. The

results show that, after controlling for these fluctuations, there is no correlation between business

cycle volatility and growth. Otherwise, there would be a significantly negative correlation,

especially for developing countries, as documented in the literature. The results have

implications for stabilization policies, and also for cross-country growth regressions in that

ignoring heterogeneity among countries may lead to wrong conclusions.

JEL Classification Codes: E32, F44, O11, O40.

Keywords: Growth, Business cycles, Volatility, Volatility persistence.

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Business-cycle Volatility and Long-run Growth: How Strong is the Relationship?

1. Introduction

This paper revisits the empirical relationship between business-cycle (BC) volatility1 and

long-run growth but the key contribution lies in controlling for fluctuations in the trend growth.

Addressing these fluctuations also accounts for enormous heterogeneity among countries in their

long-run growth trajectories. The main finding is that the significant volatility-growth correlation

(or arguably the causal effect of BC volatility on long-run growth) documented in the

literature—either negative or positive—disappears after controlling for such fluctuations.

Both the theoretical and empirical literature on the relationship between BC volatility and

long-run growth lack consensus. In the Schumpeterian (1939) tradition, where the mechanism is

“creative destruction,” the effect of business cycles on long-run growth is positive. For example,

Caballero and Hammour (1994) view recessions are a time of “cleansing,” when outdated or

unprofitable techniques and products are pruned out of the productive system. During recessions

firms also accumulate “organizational capital” (Hall, 1991) and/or reallocate labor (Davis and

Haltiwanger, 1990; 1992) that induce growth in the long run.

In contrast, a negative relationship between BC volatility and long-run growth is

predicted by endogenous growth theory based on the idea of learning-by-doing or demand spill-

overs (Arrow, 1962; Stadler, 1990; Martin and Rogers, 1997). For example, business cycles

create fluctuations in employment, and the unemployed lose their skills in recessions. Therefore,

in the presence of negative learning-by-doing, temporary shocks have negative impact on long-

run growth.2 However, in the models based on the opportunity cost arguments, the prediction of

the effect of business cycles on growth can be both positive and negative (Aghion and Saint-

Paul, 1998). For example, if the cost of productivity improvements positively depends on current

production, and this cost drops by more than its present discounted benefit in a recession, then

business cycles have a positive effect on growth. Saint-Paul (1997) provides evidence at the

1 This is volatility of growth rate as opposed to volatility of level of GDP. 2 Blackburn (1999) and Blackburn and Pelloni (2004) point out that the negative relationship based on learning-by-

doing may not hold in a stochastic growth model.

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aggregate level in favor of this argument. On the other hand, if the cost of productivity-

enhancing activities does not depend on current production, the conclusion of the model reverses

and recession have a negative long-run effect.

Given the lack of consensus on the theoretical predictions, the burden is on the empirical

side to establish the actual relationship. But empirical evidence also lacks consensus. For

example, Kormendi and Meguire (1985), Grier and Tullock (1989) and Stastny and Zagler

(2007) find a positive correlation between business cycles and long-run growth. In contrast,

Ramey and Ramey (1995), Martin and Rogers (2000), Kneller and Young (2001), Fatás (2002),

Döpke (2004) and Rafferty (2005) find a negative correlation. The observed relationship also

varies across country groups. For example, Martin and Rogers (2000) find a negative

relationship for the industrialized countries but insignificant relationship for the non-

industrialized countries. They attribute learning-by-doing as a mechanism that may not be at

work for the latter group of countries.3 Imbs (2007) finds volatility and growth to be positively

related at the sectoral level but negatively related at the aggregate level. Furthermore, it has not

been established satisfactorily whether the observed relationship is a correlation or a causal

effect of BC volatility on long-run growth. It is important to point out that the theoretical models

implicitly argue for an effect of BC volatility on future growth, while the empirical studies have

tested a contemporaneous correlation.

Notwithstanding a large body of empirical research on the volatility-growth relationship,

the literature has categorically ignored fluctuations in the trend growth. The following examples

will illuminate the danger of ignoring such fluctuations in estimation. Consider two countries—A

and B—with identical average growth performances over 20 years (for simplicity consider

arithmetic average). Suppose that the annual growth rate in country A alternated every year

between 2% and -2% (i.e., 2, -2, 2, -2, ---- 2, and -2), while that in country B was 2% in the first

10 years and -2% in the last 10 years. Both countries have the same average growth rate (zero)

and volatility (measured by the standard deviation which is 2.052) but patterns of the trend

growth in these two countries are clearly different. The trend growth rate in country B is seven

times as volatile as in country A (the standard deviation of the trend growth calculated using the

3 Young (1993) also argues that growth will be driven by learning-by-doing only at relatively high levels of

development.

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Hodrick-Prescott (H-P) filter is 0.270 and 1.908 in country A and B, respectively). On the other

hand, BC volatility (measured by the standard deviation of the cyclical component calculated

using the same filter) in country A is 3.5 times as large as in country B (2.001 and 0.567,

respectively). Suppose, there is another country C that experienced a -2% growth rate in the first

12 years, zero in next 2 years and 4% in the last 6 years. Although average growth in country C

is also zero and its BC volatility (0.573) is similar to that in country B, volatility of its trend

growth (2.62) is greater than that in both A and B. In Section 3, we provide similar examples

observed in the data.

The above examples illustrate that many dissimilar growth trajectories that differ in terms

of fluctuations in the trend growth can lead to the same average growth rate. By ignoring these

fluctuations, the literature also fails to address the enormous heterogeneity among countries. In

this paper, we address these fluctuations by the standard deviation of the trend (long-run) growth

rate calculated by the low-pass filter (we refer it to long-run (LR) volatility). The reason for

controlling LR volatility in estimation can also be understood from the following volatility

decomposition. Given that there are enormous transitory (cyclical) variations around the trend

growth for many countries and that the trend growth per se is also volatile, per capita real GDP

growth rate ( ,y tg ) can be written as the sum of two orthogonal terms, its business-cycle ( ,BCy tg )

and long-run components ( ,LRy tg ): , , ,

BC LRy t y t y tg g g= + .4 Its variance is then decomposed as

, , ,Var( ) Var( ) Var( )BC LRy t y t y tg g g= + .

We use this spectral relation to explore the volatility-growth relationship at the cross-

country level. Our main source of data is the PWT 8.0. We choose the 1960-2007 period because

of unavailability of data for control variables for periods earlier than 1960 and to ensure that our

results are not influenced by the recent global financial crises that started in 2008. We also

estimate for the 1960-1980, 1970-2007 and 1980-2007 sub-periods, and disaggregating by the

intensity of BC volatility and country income groups. To verify the results from an alternative

dataset and different time periods, we perform a separate analysis for the 1878-2010 period using

4 Romer (2012, p. 136) stresses that statistical tests do not determine whether growth rate is stationary or

nonstationary; rather they suggest that “there are highly transitory movements in growth that are large relative to any

long-lasting movements that may be present.” The question of stationarity is also economically unimportant.

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the historical time series compiled by Angus Maddison for a relatively small number of

countries. As an additional robustness check, we replicate Ramey and Ramey (1995, AER) using

their data.

The BC and LR volatility are calculated as the standard deviation of the cyclical and

long-run components of (annual) per capita real GDP growth rate, respectively. We extract these

two components employing the Baxter-King (B-K) (1999) filter at the business-cycle and low

frequencies, respectively. We choose a window of 3 years, and critical periodicities (inversely

related to frequencies) of 2 and 8 years for the business cycle, and 8 years and above for the

long-run. We estimate both cross-section and panel data. The cross-section data is constructed by

taking average and calculating standard deviation of the relevant variables over the sample

period. To construct the panel data, non-overlapping average over 7 years has been taken for the

annual growth rate and other series. We show that averaging over 7 years performs better in

terms of reweighting the variances of the raw series across low frequencies than averaging over 5

years as commonly done in the cross-country growth literature. BC and LR volatility have been

calculated as the standard deviation of the respective filtered growth rates over the same interval

but the filter has been modified as one-sided using only lag values so that an artificial reverse

causality from growth to volatility is not generated.

We test both the contemporaneous correlation between BC volatility and growth

following the empirical literature, and the neglected theoretical prediction of the effect of BC

volatility in the previous period on current growth. We find that there is no correlation between

BC volatility and growth. The result is robust in both cross-sectional and panel estimations, and

in both the PWT and Angus Madison datasets. But if LR volatility is incorrectly excluded from

the regression, the correlation becomes significantly negative, especially for developing

countries in the post-1970 period. There is also no effect of BC volatility in the previous period

on current growth. The direction of bias in the coefficient on BC volatility depends on the

correlation between growth rate and LR volatility excluded in the regression. Our measure of LR

volatility can also be interpreted as persistence in volatility. We find that persistence in volatility

has a negative association with growth for developing countries in the post-1970 period.

Our results have important implications for stabilization policies in light of the recent

global financial crises that caused a prolonged recession and depressed many developed

economies enough to lower the trend growth. However, such contractions are more frequent in

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developing than developed countries. Berg, Ostry and Zettelmeyer (2012) show that inequality of

the income distribution, lack of democratic institutions and macroeconomic instability are some

factors that cause shorter growth spells (prolonged and more frequent recessions). Mallick

(2014) shows that terms-of-trade volatility and financial underdevelopment cause persistent

growth volatility. But these characteristics may also be symptoms as well as propagation

mechanisms of volatility persistence. Understanding volatility persistence is crucial for designing

stabilization policies but is an under-researched area, even in the context of developed countries.

The rest of the paper proceeds as follows. Section 2 discusses the data including

construction of both BC and LR volatility. Section 3 motivates the paper by presenting examples

of heterogeneity observed across countries in terms of their growth trajectories. This section also

presents some key descriptive statistics. The estimation strategy is explained in Section 4. The

results are discussed in Section 5. Section 6 compares the relative importance of volatility and its

persistence in explaining growth. Section 7 compares the paper’s contribution in the cross-

country macroeconomic literature regarding volatility persistence. Finally, Section 8 concludes.

2. Data

In this section we explain the data used in our empirical analysis including construction

of BC and LR volatility.

The main source of data is the PWT 8.0. Average per capita growth rate and volatility

have been calculated from the RGDPNA series (the real GDP at constant national prices), which

is recommended to compare growth rates across time and countries (Feenstra, Inklaar and

Timmer, 2013, Table 5 in p. 30). Per capita real GDP (Y) is calculated by dividing RGDPNA by

population (POP). Annual growth rate is calculated as the log difference: -1ln( / )t t tdy Y Y= .

The BC and LR volatility have been calculated as the standard deviation of the cyclical

and long-run components of tdy , respectively, extracted employing the B-K filter.5 A window of

5 Levy and Dezhbakhsh (2003) and Mallick (2014) calculate BC and LR volatility using the spectral method by

integrating the spectrum over the relevant frequency ranges. However, this method requires relatively long time

series, so that it cannot be employed at our panel data analysis. Fatás (2000a, 2000b), Levy and Dezhbakhsh (2003),

Aguiar and Gopinath (2007) and Nakamura, Sergeyev and Steinsson (2012) employ the Cochrane’s (1988) variance

ratio to calculate LR volatility but this method cannot be used to calculate BC volatility. Another alternative can be

unobserved component (UC) model. For example, Stock and Watson (2007) and Ascari and Sbordone (2014)

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3 years, and critical periodicities of 2 and 8 years for cyclical components (band-pass filter), and

8 years and above for long-run components or equivalently low frequency components (low-pass

filter) have been chosen.6 The main purpose of a filter is to extract the cyclical components of a

series, and the long-run components are then recovered as the residual. But we extract the long-

run components using the low-pass filter assuming that per capita real GDP growth is stationary.

Average growth rate (Δy) is the average of tdy . For the cross-section data, we take

average of tdy , and calculate the standard deviation of the filtered series over the entire sample

period. The panel data has been constructed by non-overlapping averaging over 7 years.

Volatility calculated as the standard deviation of the filtered growth series may be problematic

for our purpose because the B-K filter is based on a (symmetric) moving average of the lead and

lag values. As a result, volatility for a particular interval also incorporates information about

growth of the preceding interval, which artificially generates a reverse causality from growth to

volatility. To avoid this problem, we transform the growth series by one-sided filter using only

the lag values, and calculate the standard deviation of this modified filtered series.

For initial level of GDP, we use the CGDPe series (expenditure-side real GDP at current

PPPs in million 2005 US$ that compares relative living standards across countries at a single

point in time), as recommended by Feenstra, Inklaar and Timmer (2013). Terms of trade (ToT) is

estimate the time varying volatility of the trend and cyclical components of inflation for the USA. This method is

not suitable at the cross-country level because iteration does not converge for many countries, especially the

developing ones.

6 Comin and Gertler (2006), Comin (2009) and Comin et al. (2014) employ a non-standard definition of long-run in

terms of the periodicity of 200 quarters and above. They refer to the periodicities between 2 and 200 quarters as the

medium-term business cycle of which periodicities between 2 and 32 quarters as the high-frequency component of

the medium-term (the standard business cycles), and frequencies between 32 and 200 quarters as the medium-

frequency component of the medium-term. The authors also show that high and medium term fluctuations of GDP

are connected. Our definition of long-run periodicities of 8 years (32 quarters) and above includes their medium-

frequency components, and we emphasize the importance of correlation between growth volatility at business cycle

and long-run periodicities. Chirinko and Mallick (2014) demonstrate in a different context that a critical periodicity

of 8 years sufficiently captures the long-run information and gain from further increasing this cut-off is negligible.

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calculated as the ratio of export to import price (PL_X / PL_M). Investment and government

expenditure shares of GDP are the CSH_I and CSH_G series, respectively.

Openness is the sum of exports and imports as a share of GDP at the current price and the

data is obtained from the PWT 7.1 (this data is not available in the PWT 8.0). Educational

attainment data is from the Barro-Lee (2013) dataset. Political violence is captured by the total

summed magnitudes of all societal and interstate major episodes of political violence (MEPV) in

a country compiled by Center for Systemic Peace.7 Private credit data has been collected from

Financial Development and Structure Dataset complied by Beck et al. (2000) and revised by

Čihák et al. (2012).

3. Heterogeneous growth trajectories: Some examples

We have earlier illustrated hypothetical examples on possible heterogeneity among

countries in their growth trajectories. In this section, we provide several examples of such

heterogeneity observed in the data in terms of growth rate, BC volatility and LR volatility for

1960-2007 period. Detail information for all sample countries is provided in Appendix A.1. We

also discuss some descriptive statistics at the end of this section.

Namibia vs. Nepal: Both countries had the same average growth rate (about 0.013) and

BC volatility (0.026), but in Namibia (0.019) LR volatility was about twice as large as in Nepal

(0.010).

Columbia vs. Australia: Both countries had almost the same average growth (0.020 vs.

0.021) and BC volatility (0.015 vs. 0.014), but in Columbia LR volatility was much larger than

in Australia (0.013 and 0.008, respectively).

7 MEPV is an annual, cross-national, time-series data on interstate, societal, and communal warfare magnitude

scores (independence, interstate, ethnic, and civil violence and warfare) for all countries. We use the ACTOTAL

series in the dataset. ACTOTAL is calculated as the sum of the magnitude score of episode(s) of: i) international

violence, ii) international warfare, iii) civil violence, iv) civil warfare, v) ethnic violence, and vi) ethnic warfare

involving that state in that year. Each type of violence/warfare is scaled from 1 (lowest) to 10 (highest) for each

MEPV; magnitude scores for multiple MEPV are summed with 0 denoting no episodes.

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Argentina vs. Burkina Faso: These two countries also differ only by their LR volatility

(0.022 vs. 0.014); otherwise, they are similar in terms of average growth (about 0.011) and BC

volatility (about 0.044).

Romania vs. Malaysia: Both countries had the same average growth (0.041). But BC

volatility was larger in Malaysia (0.033) than in Romania (0.026), while Romania (0.044) had

more than twice as large LR volatility as Malaysia (0.020).

Japan vs. Cyprus: Both countries had the same average growth (0.043). However,

compared to Cyprus, Japan experienced milder BC volatility (0.033 vs. 0.056) but greater LR

volatility (0.036 vs. 0.020).

Mauritania vs. Fiji: Both countries experienced the same average growth (0.018) but

Mauritania had much greater BC volatility (0.064 vs. 0.043) as well as LR volatility (0.039 vs.

0.017) than Fiji.

Israel vs. Egypt: The two neighbors experienced similar average growth (0.034 vs. 0.037)

but Israel had greater BC volatility (0.053 vs. 0.032) as well as LR volatility (0.036 vs. 0.015)

than Egypt.

There are also examples where similar fluctuations are related to divergent average

growth. For example, growth rate was much higher in Hong Kong (0.048) than in Bangladesh

(0.011) although both countries had the same BC volatility (0.035) and LR volatility (0.019).

Niger and Cyprus can be another likely pair. Both countries had very similar BC volatility (0.054

vs. 0.056) and LR volatility (0.025 vs. 0.020), but Niger economy declined at an average rate of

0.012, while Cyprus grew rapidly at the rate of 0.043. The heterogeneity can also be present

among developed countries. For example, for the 1970-2007 period, average growth rate and BC

volatility in Japan and Austria were the same at 0.024 and 0.014, respectively, but LR volatility

was more than twice in Japan (0.014) than in Austria (0.06).

The above examples illustrate an enormous heterogeneity among countries in their

growth trajectories. More specifically, very dissimilar growth trajectories can lead to the same

average growth. On the other hand, apparently similar growth trajectories can also lead to

different average growth. Figures 1(a)-(j) display growth trajectories of the countries mentioned

above in terms of their long-run growth rate calculated by the low-pass filter.

Insert Table 1 and Figures 1-2 here

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Average growth rate, BC volatility and LR volatility for the 1960-2007 period in a

sample of 107 countries8 are summarized in Table 1. Countries are classified as high, middle and

low income following the World Bank classification. BC volatility decreases with income

level—it is 0.046 in low income countries compared to 0.036 and 0.024 in middle (upper and

lower middle income combined) and high income countries, respectively. LR volatility is same

in both low and middle income countries (around 0.023) and slightly smaller in high income

countries (0.020). Figures 2(a)-(b) display that both BC and LR volatility decrease with initial

income level. Although BC volatility is larger than LR volatility for all income groups, the ratio

of BC volatility to LR volatility is the largest for low income countries followed by middle and

high income countries (column (4)). The correlation between BC and LR volatility along with

the 95% confidence intervals are reported in column (5). The correlation is 0.61 for all sample

countries; it is the largest for high income countries at 0.84 followed by middle and low income

countries (0.60 and 0.45, respectively). Figure 3 confirms the positive relationship between BC

and LR volatility.

4. Estimation strategies

Our estimation strategy is simple in which long-run growth is regressed on BC volatility

and a set of conditioning variables among which LR volatility is the most important one. The

cross-section specifications are given by:

1 2 ,0i C i i i i iy BCvol LRvol y vα γ γ β ′∆ = + + + + +X δ , ---(1a)

1 ,0 i U i i i iy BCvol y uα γ β ′∆ = + + + +X δ . ---(1b)

Here iy∆ is the average growth rate of real per capita GDP (explained in Section 2), ,0iy is the

log of real per capita GDP in the initial period and X is a set of conditioning variables. Our

attention is on 1Cγ , the (corrected or credible) coefficient on BC volatility ( iBCvol ) in equation

8 These 107 countries are based on the availability of RGDPNA data without any discontinuity. Among these

countries, we consider possible six outliers (based on BC and LR volatility in Appendix A.1)—Equatorial Guinea,

Iran, Rwanda, Gabon, Guinea-Bissau and Syria—but do not exclude them from the sample. The descriptive statistics

and regression results do not qualitatively change if these countries are excluded from the sample.

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(1a). We also estimate 1Uγ (the uncorrected coefficient) in equation (1b) without controlling for

LR volatility ( iLRvol ) to compare and contrast with other results in the literature. We show the

direction of bias in 1Uγ at the end of this section.

Choice of controls ( X ) in cross-country growth regressions is a difficult task given that a

large number of variables have been found to be significant in different studies. Some studies

control the variables that are robustly significant in extreme bound analysis (or Bayesian model

averaging). We take a different approach in order to avert the omitted variable bias that involves

controlling only those determinants of growth that also affect BC volatility. Omission of controls

will not cause any bias as long as they are uncorrelated with BC volatility.

The following variables are included in X : (i) investment share in GDP, (ii) (initial)

human capital measured by the year of schooling for aged over 15 years, (iii) population growth

rate, (iv) trade openness measured by the sum of exports and imports as a percentage of GDP, (v)

growth rate of government share in GDP, (vi) terms of trade (ToT) volatility measured as the

standard deviation of the ratio of the export to import prices (as a proxy for external shocks),

(vii) political violence (explained in Section 2), and ix) financial development proxied by the

credit disbursed to the private sector by banks and other financial institutions relative to GDP.

Initial (log) per capita income is also included to account for conditional convergence and the

transitional dynamics so as to avert a positive bias on the coefficient on BC volatility (Martin and

Rogers, 2000, p. 365). The controls (i)-(iii) are common in growth-volatility regressions (for

example, Ramey and Ramey, 1995) but can also be justified by economic reasoning. Investment

is crucial for economic growth but it is also the most volatile component of GDP over business

cycles. Higher population growth can cause economic (and political) instability in a country

unless accompanied by economic growth faster enough to reduce unemployment.9 Higher human

capital, although plays an important role in economic growth, also cause economic and political

instability if left unutilized—the Arab Spring is a recent example (Kuhn, 2012).

The role of openness in economic growth is established both theoretically and empirically

but openness also affects volatility. Using an industry-level panel dataset of manufacturing

9 Higher population growth has also been found to be related to higher consumption volatility (Bekaert, Harvey and

Lundblad, 2006).

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production and trade, Giovanni and Levchenko (2009) document a positive and economically

significant relationship between trade openness and overall volatility. Mallick (2014) also

observes similar effects using aggregate data at the cross-country level. Kose, Prasad and

Terrones (2006) find out that openness stimulates both growth and volatility.

Growth of the share in government expenditure is intended to account for government

expenditure shocks documented in the Real Business Cycle literature.

Easterly et al. (1993) document that shocks, measured by the change in the ToT,

influence growth directly and also indirectly through policy variables. A negative robust impact

of the change in the ToT on growth volatility is documented by Mallick (2014) and Agénor et al.

(2000). Mendoza (1995) quantifies ToT shocks as accounting for 40%-60% of the observed

variability of GDP at the cross-country level. Koren and Tenreyro (2007) find strong negative

correlations between growth and volatility of country level macro shocks.

Rodrick (1999) show that domestic social conflicts are a key to understanding lack of

persistence in growth performance and growth collapse since the mid-1970s. Social conflicts

interact with external shocks and the domestic institutions of conflict-management. Acemoglu et

al. (2003) argue that bad macroeconomic policies that increase volatility and lower growth are

the results of weak institutions, which is also related to social and political instability.10 Ploeg

and Poelhekke (2009) show that ethnic tensions cause higher volatility and lower growth.11

Financial development is one of the main channels through which volatility affects growth

(Aghion and Banerjee, 2005).

The above list of variables is certainly not a complete one. There may be other variables

that trigger both growth and BC volatility. It is conceivable that many omitted variables are

related to the level of economic development, and therefore controlling for initial income level in

the regression, to a large extent, captures these omitted variables. We additionally include region

dummies (Latin America, Sub-Saharan Africa, Asia Pacific, and Middle East and North Africa)

10 We think that political violence, to a large extent, captures the institutional development. Nonetheless, we also

additionally control for Polity2 to verify robustness, especially for developing countries.

11 In investigating the effect of uncertainty on growth, Baker and Bloom (2013) used natural disasters, terrorist

attacks and unexpected political shocks as instruments of uncertainty measured by the first and second moments of

the stock prices. However, the authors recognize the endogeneity of these shocks in the long run.

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in the regression as some regions are more volatile than others for reasons not discussed above;

these dummies also capture omitted variables in growth regressions (Berg, Ostry and

Zettelmeyer, 2012). Finally, we include dummies for legal origins and landlocked to account for

country fixed effects as well as omitted variables. For example, La Porta et al. (1997; 2008)

document that financial development of a country is greatly influenced by its legal origin.

Financial development data is not available for many developing countries before 1980.

Therefore, in the specification that exclude financial development, legal origin dummies act as

proxies. Growth performance of landlocked countries is dismal and these countries also

experience greater volatility as a result of lack of access to the market (Malik and Temple, 2009).

We construct three cross-sectional datasets for the 1960-2007, 1970-2007 and 1980-2007

periods, respectively, to verify stability of the results across time periods and sample countries

(fewer countries are retained in the 1960-2007 period because of unavailability of data for some

control variables).

The cross-sectional estimation captures the “between” country variations. Panel data

allows a richer investigation by also capturing the “within” country variations. The estimating

equations are written as:

0, 1 , 2 , 1 , , 1 .i C i i i i i iy BCvol LRvol y vτ τ τ τ τ τ τα γ γ β µ η−′∆ = + + + + + + +X δ , ---(2a)

0, 1 , 1 , , 1 , i U i i i i iy BCvol y uτ τ τ τ τ τα γ β µ η−′∆ = + + + + + +X δ . ---(2b)

Here, iµ is the country fixed effects captured by dummies for legal origins and landlocked, τη is

the aggregate time effects captured by time dummies and 0,iy τ is the log of real per capita GDP in

the initial year of each interval. All control variables are lagged by one period ( , 1i τ −X ).

Equation (2a), like equation (1a), will estimate a correlation between BC volatility and

growth. To estimate a casual effect, we need to correct the endogeneity due mainly to reverse

causality from growth to BC volatility. The reverse causality can be both negative and positive.

For example, in Aghion and Banerjee (2005), higher growth leads to volatility. Investment and

borrowing are higher in a boom, leading to higher interest rates. This in turn creates a pecuniary

externality by increasing the debt burden of all entrepreneurs, constraining the growth of

entrepreneurial wealth and investment capacity. At some point, investment capacity falls below

total savings, the economy recedes, and interest rates decrease. The process then reverts to a

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boom.12 Lack of growth may also cause political instability that in turn leads to economic

instability. Endogeneity in LR volatility will also bias the coefficient on BC volatility.

Instrumental variable estimation is the solution but it is almost impossible to find exclusion

restrictions for identification in the cross-country growth regressions in the sense that some

exogenous variables affect long-run growth only through BC volatility (unless someone is lucky

enough to find a natural experiment).13 Lagged values are potential candidates for instruments of

contemporaneous values in the panel data. But, as implicit in the literature discussed in

introduction, lagged BC volatility affects growth through cleansing/reallocation effect or

learning-by-doing, so they cannot be valid instruments.14

One way to solve the reverse causality problem is to directly include lagged volatility in

the regression instead of contemporaneous values. This procedure also tests the theoretical

12 However, the authors also argue that this can happen only at certain level of financial development. Credit

constraint is very high in a highly financially underdeveloped country, so that entrepreneurs rely entirely on their

retained earnings for investment. Conversely, in financially developed countries, firms face no credit constraints and

thus can invest up to the expected net present value of their projects. Therefore, financially developed or

underdeveloped countries will not experience volatility; the remaining countries at the intermediate level of financial

development are vulnerable to volatility.

13 Several studies have tried to establish causality from BC volatility to growth using the instrumental variable

regressions. For example, Hnatkovska and Loayza (2005) used the following variables as the instruments of

volatility: the standard deviation of the inflation rate, a measure of real exchange rate misalignment, the standard

deviation of ToT shocks, and the frequency of systematic banking crises. Martin and Rogers (2000) used the

standard deviation of the growth rate of the preceding decade, the initial inflation rate of the decade, the initial level

of GDP per capita and the number of revolutions and coups as instruments for the developing countries. Mobarak

(2005) used diversification as the instrument of volatility. However, exogeneity of these instruments in the long run

can be disputed. Bazzi and Clemens (2013) provide an excellent discussion on the problem of instrument variable

estimation in cross-country growth regressions.

14 A matrix of instruments following the Arellano and Bond (1991) or Blundell and Bond (1998) dynamic panel

estimation using lagged level and differences could also be constructed in a static panel. In addition to the direct

effect of lagged volatility on growth, these instruments also suffer from weak instrument problem because the

requirement for instrumental strength that the variance of the residual must be larger than the variance of the fixed

effect is almost always violated in the cross-country data (see, Bazzi and Clemens, 2013; Newey and Windmeijer,

2009).

15

predictions of the effect of BC volatility in the previous period on current growth. Provided that

the omitted variable problem is satisfactorily addressed and that BC (and LR) volatility are

calculated using the growth series transformed by one-sided filter using only lag values to avoid

generated reverse causality (discussed in Section 2), the coefficient on BC volatility in the

previous period (interval) will represent a causal effect on current growth. Our identification

approach in this particular context will be more reliable than employing invalid and weak

instruments.15 The following specifications are estimated to obtain a causal effect:

0, 1 , 1 2 , 1 1 , , 1 .i C i i i i i iy BCvol LRvol y vτ τ τ τ τ τ τα γ γ β µ η− − −′∆ = + + + + + + +X δ , ---(3a)

0, 1 , 1 1 , , 1 , i U i i i i iy BCvol y uτ τ τ τ τ τα γ β µ η− −′∆ = + + + + + +X δ . ---(3b)

Since . , 1 . , 1 . , 1( , ) ( , ) ( , ) 0i i i i i iCov v BCvol Cov v LRvol Cov vτ τ τ τ τ τ− − −= = =X , pooled OLS regression

will obtain consistent estimates. The standard errors are clustered at the country level.

Finally, we estimate correlation (both contemporaneous and lagged) at longer horizon

using the historical data constructed by Angus Maddison. We choose the 1875-2010 period in

order to retain a relatively large number of countries in the sample. We first calculate the annual

growth rate by log-differencing per capita real GDP and then construct a 7-year panel data

similar to that constructed in the PWT data. We control only for the (log) initial per capita GDP,

time dummies and dummies for the pre-1914, 1914-1945, 1946-1985; and post-1985 periods,16

as other controls are not available for such a long period.

To know the direction of bias in the coefficient on BC volatility when LR volatility is

incorrectly excluded from the regression, simplify equations (1a)-(1b) excluding the controls:

1 2i C i i iy BCvol LRvol vα γ γ∆ = + + + , ---(4a)

15 The correlation between volatility and growth is arguably no less important than the causal effect. In another

context, Acemoglu, Hassan and Robinson (2011) estimate correlation between the severity of the persecution,

displacement, and mass murder of Jews due to the Holocaust and long-run economic and political outcomes in

Russia because of the lack of exogenous instruments.

16 Romer (2012, p. 192) suggested that macroeconomic history of the USA since the late 1800s consists of four

broad periods: i) before the Great Depression, ii) the Great Depression and World War II, iii) at the end of the World

War II to about mid-1980s, and iv) after mid-1980s. This classification can be readily generalized to other sample

countries except for the first period due to the World War I. Therefore, we modify the first period accordingly.

16

1 i U i iy BCvol uα γ∆ = + + . ---(4b)

The estimated coefficient on BC volatility in equations (4a) and (4b) can be expressed,

respectively, as:

[ ]1 2corr( , ) corr( , )*corr( , ) Var( )ˆ *

Var( )1 corr( , )C

y BCvol y LRvol BCvol LRvol yBCvolBCvol LRvol

γ ∆ − ∆ ∆=

−, ---(5a)

and 1Var( )ˆ corr( , )*

Var( )Uyy BCvol

BCvolγ ∆

= ∆ . ---(5b)

In the data, corr(BCvol, LRvol) >0. Therefore, the direction of bias in 1̂Uγ depends on the sign of

corr(Δy, LRvol) or, equivalently, the sign of 2γ in equation (4a). If corr(Δy, LRvol) < 0, 1̂Uγ will

be biased downward (i.e., if 1̂Cγ is positive, 1̂Uγ will move towards 0 (or even can become

negative); if 1̂Cγ is negative, 1̂Uγ will increase in absolute value with the negative sign). Similarly,

if corr(Δy, LRvol) > 0, 1̂Uγ will be biased upward (i.e., if 1̂Cγ is positive, 1̂Uγ will be larger; if 1̂Cγ

is negative, 1̂Uγ will move towards 0). Even if corr(Δy, LRvol) = 0, 1̂Uγ will still be biased upward

because of corr(BCvol, LRvol) >0 (in the denominator).

5. Results

We report 1̂Cγ and 1̂Uγ estimated from cross-sectional and panel data for different time

periods and countries. The former represents a credible correlation of BC volatility (or a causal

effect of lagged BC volatility), while the latter represents a biased correlation. We also report 2γ̂ ,

the coefficient on LR volatility, to judge its merit relative to 1̂Cγ in explaining growth, and to

show the direction of bias in 1̂Uγ . This allows both treatment of the issues we intend to address

and a direct comparison with other results in the literature.

5.1 Correlation in cross-sectional data

17

The OLS results are summarized in Table 2 for the full (1960-2007), 1960-1980, 1970-

2007 and 1980-2007 periods.17 The odd-numbered columns report 1̂Cγ (and also 2γ̂ ) estimated

from equation (1a). In all periods, 1̂Cγ is close to zero and insignificant (and also no pattern in its

sign) suggesting a lack of correlation between BC volatility and growth. As mentioned earlier,

private credit data are available for a good number of developing countries only after 1980.

Therefore, we have estimated for 1980-2007 period both with and without controlling for private

credit (and Polity2) (columns (5) and (7), respectively). The results are robust in both

specifications.

The even-numbered columns present 1̂Uγ estimated from equation (1b). It is large

negative and statistically significant in 1970-2007 and 1980-2007 periods (columns (6) and (8),

respectively). It is larger in absolute value and significant at higher level if private credit is not

controlled for (column (10)). This result suggests the importance of financial development as an

important channel through which BC volatility interacts with growth.18 With a negative (and

significant) 2γ̂ in equation (1a), 1̂Uγ is biased downward as shown in equations 5(a)-5(b).

Comparing the results from equations (1a) and (1b) for the 1970-2007 period, the coefficient of

BC volatility changes from -0.002 to -0.121. The quantitative implications of this difference is

huge. One standard deviation increase in BC volatility is associated with only 0.003 percentage

point decrease in long-run growth, which is statistically insignificant and also economically

trivial. But if the correlation of LR volatility is removed from the regression, the same increase in

BC volatility would incorrectly be associated with 0.219 percentage point decrease in long-run

growth.

Insert Table 2 here

17 The full sample period reduces to 1964-2004 because the first observation is lost after calculating growth rate

from level, and then the next three observations are lost because of employing a one-sided filter with a 3-year

window.

18 If investment is excluded, the coefficient on BC volatility hardly changes suggesting that investment is not an

important channel, which is also consistent with Ramey and Ramey (1995).

18

One might suspect that the results from equation (1a) are driven by multicollinearity

between BC and LR volatility. For example, in the 1980-2007 period, 1̂Cγ is 0.053 (positive

though very close to 0 and insignificant), but 1̂Uγ is -0.157 (significant at 10% level) after

removing the correlation of LR volatility. We rule out such a possibility by calculating the

variance inflation factor (VIF) (alternatively, tolerance = 1/VIF). The VIFs (tolerances) of BC

and LR volatility are 2.85 (0.351) and 2.80 (0.357), respectively, which are far less (higher) than

any conventionally considered critical level. Even if only BC and LR volatility are included in

the regression excluding other controls, the VIF (tolerance) is even lower (higher) at 2.31

(0.432).

To further address heterogeneity among countries for reasons other than fluctuations in

the trend growth, we perform disaggregated analysis in several ways. First, we divide the sample

countries into three groups in terms of their intensity of BC volatility: i) least volatile (0-33

percentile), ii) moderately volatile (33-66 percentile), and iii) most volatile (67-100 percentile).

There are 30 countries in each group in the full period, and 36, 35 and 36 countries, respectively,

in both 1970-2007 and 1980-2007 periods. We construct dummies for each volatility group and

interact them with BC volatility. The results are summarized in Table 3. There is no correlation

between BC volatility and growth for any of these three groups, and it is robust across time

periods and sample countries. However, if the correlation of LR volatility is incorrectly removed,

1̂Uγ becomes significantly negative for the most volatile group of countries in both 1970-2007

and 1980-2007 periods.

We now estimate equations (1a)-1(b) disaggregating by income level. The results for

developing (low and middle income combined) countries, summarized in Table 4, are similar to

those for all countries in that there is no correlation between BC volatility and growth. When

developing countries are further disaggregated into three similar groups by their intensity of BC

volatility as the full sample countries, the results are also qualitatively similar (Table 5). There is

also no significant correlation for developed (high income) countries, and the sign of 1̂Cγ changes

across periods (Table 6).

Insert Tables 3-6 here

19

The above results indicate an absence of relationship between BC volatility and long-run

growth. However, if the correlation of LR volatility is incorrectly removed, the results are

aligned to the literature to indicate a significant negative relationship especially for developing

countries in the post-1970 period.

5.2 Correlation in cross-sectional data for alternative frequency bands and filtering

Previous estimations are based on the implicit assumption that both developed and

developing countries are characterized by similar cyclical patterns. Although there is a large

literature on business cycles in the context of developed countries, very little is known about

business cycles in developing countries. Agénor McDermott and Prasad (2000) point out that

there are both similarities (procyclical real wages, countercyclical variation in government

expenditures) and differences (countercyclical variation in the velocity of monetary aggregates)

between macroeconomic fluctuations in developing and developed countries. Rand and Tarp

(2002) demonstrate that developing countries differ considerably in terms of the nature and

characteristics of short-run macroeconomic fluctuations. Analyzing a sample of 15 developing

countries (five countries each from sub-Saharan Africa, Latin America, and Asia and North

Africa), the authors document that average lengths of expansion and contraction are 4.8 and 5.2

years, respectively. This suggests that cycles are generally shorter in developing countries. Male

(2009) contrasts this conclusion but stresses that there is heterogeneity at the regional level in

that cycles are shorter in Latin America and longer in Asia.

We now calculate BC and LR volatility using an alternative critical periodicity of 5 years

for developing countries but retain the same critical periodicity for developed countries. The

results, summarized in Appendix A.2, are qualitatively similar to their benchmark counterparts

based on the B-K filter for both the full sample (Panel A) and developing countries (Panel B).

We also calculate BC and LR volatility using the Hodrick Prescott (1997) and Christiano

and Fitzgerald (2003) band-pass filters. These filters extract the cyclical components, and the

trend is retrieved as the residual. Although the H-P filter is optimal for an I(2) process and the C-

F filter is optimal for a random walk process, we nonetheless employ them to verify the

robustness of the results. We use the same window and periodicity in the C-F filter as we have

used in the B-K filter. For the H-P filter, we use a smoothing parameter of 6.25 based on the

recommendation by Ravn and Uhlig (2002, p. 371) that the parameter should be adjusted

20

approximately with the fourth power of the frequency change.19 The results using both the H-P

and C-F filters (Appendices A.3 and A.4, respectively) are very similar to the benchmark results.

5.3 Correlation and causation in panel data

Before presenting the results, it is imperative to explain the reasons for constructing a 7-

year panel. A common practice is to take 5-year non-overlapping average of annual growth rate

to calculate its long-run value (some papers also take 10-year average for robustness check).

Using the spectral density, we show in Appendix A.5 that data averaged over 5-year period does

not reweight the variances of the raw series enough across low frequencies, thus data are

contaminated by high frequencies. This contamination decreases substantially in the case of 7-

year averaging. Further improvement is small for averaging over longer horizon, such as 8 or 10

years. Since averaging over longer horizon leaves fewer observations for estimation, we choose

7 years as an optimal compromise. Note that a window of 3 years is also chosen for annual data

in the B-K filter, which is equivalent to averaging over 7 years.

We estimate equations (2a)-3(b) by pooled OLS for both full period (1960-2007) and

1978-2007 sub-period.20 The results for all countries for these two periods are summarized in

Panels A and B in Table 7, respectively. Columns (1)-(4) present the results for the

(contemporaneous) correlation estimated from equations (2a)-(2b); the first two columns control

for private credit (and Polity2), while the last two do not (so the number of observations

increases; and this can also be a test for stability of the results across countries). Columns (5)-(8)

present the effect of lagged BC volatility estimated from equations (3a)-(3b). The coefficient of

BC volatility is insignificant and small in magnitude, thus suggesting a lack of correlation

between BC volatility and growth. There is also no effect of lagged BC volatility on growth as

suggested by its insignificant (and close to zero) coefficient. The results follow similar patterns

for developing countries (Table 8). In both Tables 7 and 8, the correlation becomes significantly

negative and larger in magnitude if LR volatility is incorrectly excluded from the regression. For

developed countries, the results are also similar except that there is a positive correlation of BC

19 STATA also recommends a smoothing parameter of 6.25 for annual data. 20 The effective sample periods 1964-2007 and 1978-2007 cannot be divided into seven equal intervals; for the last

interval, we take average over 9 years (1999-2007).

21

volatility in the 1978-2004 period (Table 9). The significance of the correlation does not change

after controlling for LR volatility because of small (and insignificant) value of 2γ̂ (0.10).

Insert Tables 7-9 here

To summarize, the results in the panel data corroborate the main conclusion in the cross-

sectional data. In addition, there is no significant effect of lagged BC volatility on growth. All

the results remain robust (not reported) if the two-sided symmetric filter is used to calculate BC

and LR volatility.

5.4 Correlation in the historical (1878-2010) panel data

We now estimate the relationship using the historical data compiled by Angus Maddison

for the 1875-2010 period.21 This estimation allows us to verify the results from an alternative

dataset and time period. A 7-year panel is constructed similar to the PWT data. There are 28

countries of which 20 are developed by the current income level (A list of countries is provided

in the note for Table 10), and there are 18 observations for each country.22 Due to unavailability

of data for control variables, we control only (log) initial level of GDP, time dummies, and

dummies for major economic episodes: pre-1914, 1914-1945, 1946-1985, and post-1985 periods.

As a result, country fixed effects will be correlated with the omitted variables, so we estimate the

fixed effect regression. We interpret both the coefficients on BC volatility and its lag as

correlation.

Insert Table 10 here

21 Data goes back to earlier period but the number of countries decreases. For example, data is available since 1820

for only 8 countries (Australia, Italy, Denmark, France, Netherlands, Sweden, UK and USA).

22 In the dataset, consecutive values of real per capita GDP since 1875 are available for 28 countries. The actual time

period retained in the analysis is 1879-2010 because the first observation is lost due to calculation of growth rate

from level of GDP, and next three observations are lost due to using the one-sided filter. The time period is then

divided into 18 equal 7-year intervals except the last interval (2004-2010).

22

Panels A and B in Table 10 summarize the results for full sample, and 20 developed

countries, respectively. The results are similar in both panels. There is no contemporaneous or

lagged correlation between BC volatility and growth. The correlation becomes negative and

significant, and the lagged correlation becomes positive and significant after incorrectly

removing correlation of LR volatility and its lag, respectively.

5.5 Replication of Ramey and Ramey (1995)

Our final robustness check is to replicate Ramey and Ramey (1995), arguably the most

influential study on the volatility-growth relationship, using their data and controls. We replicate

their basic cross-sectional specification, which is comparable to our specification. Using the

PWT 5.6 data, Ramey and Ramey estimated the relationship for two sets of countries: a full

sample of 92 countries for the 1960-1985 period, and 24 OECD countries for the 1950-1988

period. It is worth mentioning that the PWT data has been revised several times and subsequent

revisions are not strictly comparable. Ponomareva and Katayama (2010) replicated Ramey and

Ramey and found that conclusions based on one version of the PWT may not hold under another

version; however, growth and uncertainty are negatively and significantly related for countries

with the worst data quality.23

Ramey and Ramey calculated growth rate (and volatility) from the “Real GDP per capita,

1985 international prices: Chain Index (RGDPCH)” (their Data Appendix, p. 1150). This is not

the appropriate variable to compare the growth rates over time and across countries; the

appropriate variable is the growth of GDP at constant national prices (also strongly

recommended by Feenstra, Inklaar and Timmer (2013) in the PWT 8.0 user guide, p. 25). GDP

at constant national prices data was not available in the PWT 5.6, so Ramey and Ramey

conducted the best possible exercise given the data. We therefore additionally replicate Ramey

and Ramey using the growth of GDP at constant national prices from the PWT 8.0 for the same

23 Dawson et al. (2001) also replicated Ramey and Ramey (1995) and found that the results do not hold after

controlling for data quality.

23

countries and time period. However, this can be done only for their 24 OECD countries as data is

not available for a good number of countries in their full sample.24

Insert Table 11 here

The results are summarized in Table 11. Panel A reports the results for 92 countries for the 1960-

1985 period. In column (1), the coefficient on volatility (standard deviation of the growth rate) in

the specification without any control reported by Ramey and Ramey is reproduced—it is -0.15

with a t-statistic of -2.3 (it becomes -2.6 after correcting heteroskedasticity). However, as we

discuss in detail in Section 6, the standard deviation of the growth rate differ from our measure

of BC volatility (the standard deviation of the business cycles components of growth rate). In the

same specification, the coefficient on BC volatility is very close at -0.16 with a t-statistic of -2.59

(column (2)). When their controls— initial income, average population growth, average

investment share of GDP and initial human capital—are included in the regression, the

coefficient on BC volatility decreases to -0.109 with a t-statistic of -1.636 (which slightly falls

short of 10% level significance) (column (3)). But after controlling for LR volatility, the

coefficient on BC volatility is almost zero (0.006) with a very low t-statistic of 0.066 (column

(4)).

The results for the 24 OECD countries are summarized in Panel B. The coefficient on BC

volatility in the specification with all controls is large negative (-0.41) and significant (t-value of

-2.46), and does not meaningfully change after controlling for LR volatility (columns (3) and (4))

(the coefficient on LR volatility is positive but insignificant). However, when we replicate these

results (with same countries, time period and controls) using the growth of GDP at constant

national prices data from the PWT 8.0 (Panel C), the coefficient on BC volatility is small and

24 In the PWT 8.0, data are not available for the following 9 countries in the Ramey and Ramey sample:

Afghanistan, Algeria, Guyana, Haiti, Myanmar (Burma), Nicaragua, Papua New Guinea, Yugoslavia (country

disintegrated), and Zaire. For Iraq, Sudan and Swaziland, GDP data starts from 1970, and for Liberia from 1964.

Therefore, a total of 13 countries are missing from the sample.

24

statistically insignificant both without and with controlling for LR volatility, and the sign differs

in the two specifications. These results are perfectly in line with our previous results, and

suggests a lack of relationship between BC volatility and growth.

6. Volatility vs. its persistence

LR volatility is also interpreted as persistence in volatility (Levy and Dezhbakhsh, 2003;

Ascari and Sbordone, 2014). In the following, we compare the relative importance of BC

volatility and persistence in volatility in explaining long-run growth.

We have found that there is no correlation between BC volatility and growth, and no

effect of lagged BC volatility on growth. But the correlation becomes significant and stronger if

LR volatility is incorrectly excluded from regression. Moreover, the results show a negative and

significant correlation between LR volatility and growth, especially for developing countries and

in the post-1970 period. On the other hand, the correlation is positive in the 1960-1980 period

but not robust across country income groups. It is positive for developed countries in the post-

1970 period but not robust to estimation methods. The correlation is weakly negative in the

Angus Madison panel data (Table 10). The effect of lagged LR volatility is positive for

developed countries (Table 9, Panel B and Table 10). These findings signify the importance of

LR volatility in explaining growth. They also imply that if LR volatility is omitted from the

regression, its effect, to a large extent, will be reflected in the coefficient of BC volatility.

Several studies (for example, Ramey and Ramey, 1995) use standard deviation of

(unfiltered or raw) growth rate as a proxy for BC volatility. This measure is based on the

assumption of a constant trend, while BC volatility calculated as the standard deviation of the

cyclical components of growth assumes a time varying trend. As shown in introduction, total

variance of growth rate is sum of the variances of its cyclical and long-run components.

Therefore, volatility measured as the standard deviation of growth rate will capture the combined

effects of both BC and LR volatility. In other words, both the standard deviation of the cyclical

components of growth (in misspecified regression that excludes LR volatility) and that of the

(unfiltered or raw) growth will capture the effect of LR volatility.

Insert Table 12 here

25

To verify the above argument, we estimate correlation (and effect) of total volatility

defined as the standard deviation of (unfiltered or raw) growth rate. The results for some selected

specifications based on the significance of 2γ̂ (coefficient on LR volatility) and/or 1̂Uγ

(uncorrected coefficient on BC volatility) are presented in Table 12. Consider the cross-sectional

results for 1970-2007 period presented in columns (1)-(3) in Panel A. The first two columns

reproduce the results from columns (5) and (6) in Table 2, respectively. In column (3) we add the

result for total volatility (based on the same specification). The coefficient on total volatility is

negative and significant. Quantifying the result, one standard deviation increase in total volatility

is associated with 0.263 percentage point decrease in growth. On the other hand, 1̂Cγ (corrected

coefficient on BC volatility) was insignificant but 2γ̂ was negative and significant. The latter

result can be quantified as 0.297 percentage point decrease in growth for one standard deviation

increase in LR volatility. But 1̂Uγ became negative and significant after omitting LR volatility in

the regression—it implied that one standard deviation increase in BC volatility was incorrectly

associated with 0.219 percentage point decrease in growth. These results support our argument

that the contribution of LR volatility is misconstrued as the contribution of total volatility or that

of BC volatility because of misspecification.

To summarize, it is not BC volatility but persistence in volatility that is associated with

growth, and the association differs across time periods and country groups.

7. Relating the contribution in the literature

Our paper is situated in a large body of literature on the volatility-growth relationship but

can be distinguished by its contribution in accounting for the persistence in growth volatility.

The issue of persistent fluctuations has been raised in the cross-country macroeconomic literature

in several contexts. In the following, we compare and contrast our contributions in this literature.

Fatás (2000a, 2000b) document a strong positive correlation between long-run growth

rates and persistence of output (not growth) fluctuations in a cross section of countries. The

results suggest that volatility of the permanent component of output is larger for countries with

high growth rates. In contrast, we deal with a different question regarding growth volatility and

document that the relationship between growth and persistence in growth volatility differ across

time periods and country groups.

26

Some studies have distinguished volatility between its unexpected (uncertain) and

expected components. It is imperative to distinguish between uncertainty in, and volatility of,

growth. Uncertainty accounts for only the unpredicted component of growth, while volatility

accounts for both predicted and unpredicted components (Wolf, 2005).25 Uncertainty is usually

calculated as the residual of a forecasting equation where GDP growth is regressed on its own

lags and linear (and quadratic) trends (see, Ramey and Ramey, 1995; Fatás, 2002; Rafferty,

2005). Although introducing the trends removes low frequency movements from the data and

therefore is comparable to the band-pass filtered growth, BC volatility in our paper is a measure

of ex post realized volatility as opposed to uncertainty. Ramey and Ramey (1995) and Rafferty

(2005) included in the regression both unexpected and expected volatility, where the latter was

calculated as the standard deviation of the fitted value of growth rate. Our measure of LR

volatility is different from the expected volatility in the same way as low-pass filtering differs

from fitting. The aim of low-pass filtering is to retain slow-moving values, whereas fitting

concentrates on achieving as close a match of data values as possible. Furthermore, filtering,

unlike fitting, does not involve use of an explicit function form. These differences are also

manifest in the differences in results discussed below.

Ramey and Ramey (1995) found that both the coefficients on unexpected and expected

volatility were insignificant (negative and a low t-statistic) in a sample of 92 countries. On the

other hand, in a sub-sample of OECD countries, the coefficient on unexpected volatility was

negative and highly significant, and the coefficient on expected volatility was positive and

significant. Kormendi and Meguire (1984) earlier found that standard deviation of monetary

shocks has a significant negative effect and standard deviation of growth rate has a significant

positive effect on growth. Ramey and Ramey (1995) conjectured that the standard deviation of

monetary shocks may be correlated with unexpected volatility. Thus, the positive effect of the

standard deviation of output in Kormendi and Meguire may be capturing the effect of predictable

movements in growth, similar to their expected volatility. On the other hand, we find a lack of

correlation between BC volatility and growth, and a negative and significant correlation between

LR volatility and growth, especially for developing countries in the post-1970 period. Similarly,

using the Angus Maddison historical data for 18 developed countries for the 1880-1990 period,

Rafferty (2005) found that unexpected volatility reduces, and expected volatility increases, long-

25 Bloom (2014) discusses different measures of uncertainty employed in the literature.

27

run growth. Using the same data, we instead find no association (and effect) of BC volatility, and

a weak negative association of LR volatility with growth.

Hnatkovska and Loayza (2005) distinguish between “regular” and “crisis” volatility and

show that only “crisis” volatility is statistically significant for explaining growth when both types

of volatility are included in the regression. The authors define “crisis” volatility as the portion of

the standard deviation of GDP growth that corresponds to downward deviations below a certain

threshold. They set the threshold equal to one standard deviation of the world distribution of

overall volatility measures. Regular volatility, on the other hand, is defined as the portion of the

standard deviation of GDP growth corresponding to deviations that fall within the threshold.

Their distinction of the two types of volatility can be compared to our disaggregation of

countries in terms of their intensity of BC volatility. But our contribution lies in accounting for

LR volatility for which Hnatkovska and Loayza have no counterpart.

Aguiar and Gopinath (2007) point out that shocks to trend growth can be the primary

source of fluctuations in the emerging market economies as opposed to transitory fluctuations

around the trend. The authors document that these economies on average have a business cycle

twice as volatile as that of their developed counterparts. They measured business cycle by

volatility of the H-P band-passed filtered log output, and volatility of the first difference of

unfiltered log output, which corresponds to our measure total volatility in Section 6. They also

document that the first-order autocorrelation of unfiltered output growth is twice as large,

suggesting greater persistence in business cycles in emerging economies (their Table 1, p. 74).

Although our study differs from theirs in regard to the research question, we document in Table

1 that both BC and LR volatility decrease with income level, but so does their ratio. This implies

that LR volatility relative to BC volatility is also larger in developed than in developing

countries.

Our paper is also situated in a burgeoning literature on growth spells first pioneered by

Pritchett (2000).26 Pritchett pointed out heterogeneity among countries in terms of instability in

growth rates over time. Country experiences differ enormously by steady growth, rapid growth

followed by stagnation, rapid growth followed by decline or even catastrophic falls, continuous

26 Some recent papers have attempted to explore the determinants of the growth spells (for example, Berg, Ostry and

Zettelmeyer, 2012; Bluhm, Crombrugghe and Szirmai, 2014).

28

stagnation, or steady decline. He cautioned that econometric growth literature using the panel

nature of data may be uninformative to account for the heterogeneity. Our motivation and

approach to account for heterogeneity address this concern.

8. Concluding remarks

This paper finds that at the cross-country level there is no relationship between BC

volatility and long-run growth. The main departure from the extant empirical literature is in

accounting for fluctuations in the trend growth that we refer to as LR volatility. However, a

significant negative relationship can be found, especially for developing countries, if LR

volatility is incorrectly excluded from regression, which is consistent with the findings in the

literature. Our measure of LR volatility—standard deviation of the low-pass filtered growth

rate—also represents persistence in volatility. We find that persistence in volatility is negatively

associated with growth, especially for developing countries in the post-1970 period. We also test

the theoretical prediction of the effect of BC volatility in previous period on current growth but

do not find any such effect. There might be an asymmetry in the effect of BC volatility in that

volatility in expansionary and contractionary phases may have differential impacts on growth,

which can be an interesting topic to explore further.

Our results have important implications for stabilization policies in light of the recent

global financial crises. The large decline in output and very slow recovery after the 2008

recession compared to the previous recessions suggest a reduction in the trend growth rate in

many developed countries. But such contractions are more frequent in developing countries.

Causes and remedies of such fluctuations are largely unknown and require further investigation.

Our finding of lack of (or weak) correlation between BC volatility and growth does not

necessarily imply irrelevance of stabilizing business cycles since cyclical fluctuations may affect

heterogeneous agents differently that is not evident at the aggregate data.27 Our results have also

27 Lucas (1987) documented that the welfare effects of eliminating business cycle are very small, well below 1% of

national income. Krusell and Smith (1999) investigate these effects in a model with substantial consumer

heterogeneity that arises from uninsurable and idiosyncratic uncertainty in preferences and employment status. The

results suggested a welfare loss larger than Lucas (1987), but still very small. However, this model is based on the

assumption that individual shocks are unaffected by the removal of the cycles. If this assumption is relaxed, the

29

important implications for cross-country growth regressions in that ignoring heterogeneity

among countries may lead to wrong conclusions.

average gain from eliminating cycles is as much as 1% in consumption equivalents, which is large for both the poor

and rich (Krusell et al., 2009).

30

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40

Tables

Table 1: Descriptive statistics (1960-2007)

Income group Growth rate BC volatility LR volatility Ratio of BC volatility to LR

volatility

Correlation between BC and

LR volatility

Number of countries

(1) (2) (3) (4) (5) (6) All 0.021 (0.017) 0.035 (0.019) 0.023 (0.012) 1.659 (0.703) 0.612

[0.477 0.718] 107

High income 0.033 (0.013) 0.024 (0.016) 0.020 (0.017) 1.378 (0.499) 0.842 [0.702 0.920]

33

Middle and low income

0.015 (0.016) 0.040 (0.019) 0.024 (0.010) 1.783 (0.747) 0.509 [0.317 0.661]

74

Middle (upper + lower) income

0.021 (0.015) 0.036 (0.016) 0.024 (0.010) 1.591 (0.620) 0.603 [0.388 0.756]

49

Upper-middle income

0.025 (0.016) 0.037 (0.017) 0.026 (0.010) 1.484 (0.409) 0.699 [0.427 0.855]

26

Lower-middle income

0.017 (0.012) 0.035 (0.016) 0.022 (0.009) 1.711 (0.788) 0.465 [0.065 0.736]

23

Low income 0.004 (0.011) 0.046 (0.021) 0.023 (0.010) 2.161 (0.838) 0.452 [0.069 0.719]

25

Figures in parentheses are standard deviations. Figures in brackets are 95% confidence interval. Note: The ratio of BC volatility to LR volatility has been calculated for each country and the average of this cross-section is reported in column (4).

41

Table-2: OLS estimation using cross-sectional data (all countries)

Variables (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 1960-2007 1960-1980 1970-2007 1980-2007χ 1980-2007 BC volatility 0.023 0.065 -0.013 0.110 -0.002 -0.121* 0.053 -0.157* 0.013 -0.171*** (0.309) (0.925) (-0.088) (0.786) (-0.025) (-1.709) (1.045) (-1.724) (0.248) (-2.848) LR volatility 0.153 0.429* -0.292** -0.458*** -0.450*** (1.076) (1.724) (-2.195) (-5.776) (-5.172) p-value of the joint significance

0.412 0.178 0.006 0.000 0.000

Adjusted R-square

0.616 0.615 0.440 0.419 0.542 0.512 0.598 0.499 0.579 0.495

Observations 90 90 89 89 107 107 103 103 107 107 Robust t-statistics are in parentheses; *** p<0.01, ** p<0.05, * p<0.1. All regressions include a constant, initial per capita GDP (log), investment-GDP ratio, initial human capital, population growth, openness, political violence, share of government expenditure, ToT volatility, and dummies for regions, legal origins and landlocked countries. χ = Private credit/GDP and Polity2 are also controlled.

Table-3: OLS estimation using cross-sectional data (all countries): Disaggregating by the intensity of BC volatility

Variables (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 1960-2007 1960-1980 1970-2007 1980-2007χ 1980-2007 BC volatility * Dummy-1

0.100 0.097 0.226 0.440 -0.233 -0.359 -0.078 -0.424 -0.061 -0.285 (0.397) (0.389) (0.409) (0.814) (-0.967) (-1.242) (-0.252) (-1.007) (-0.203) (-0.863)

BC volatility * Dummy-2

0.007 0.036 -0.189 -0.025 0.053 -0.048 -0.045 -0.325 -0.035 -0.245 (0.041) (0.209) (-0.547) (-0.073) (0.362) (-0.303) (-0.274) (-1.368) (-0.225) (-1.385)

BC volatility * Dummy-3

0.030 0.066 -0.001 0.134 -0.022 -0.137* 0.035 -0.186* 0.007 -0.180*** (0.329) (0.782) (-0.006) (0.698) (-0.315) (-1.707) (0.644) (-1.729) (0.123) (-2.792)

LR volatility 0.166 0.416* -0.278** -0.451*** -0.449*** (1.162) (1.700) (-2.245) (-5.737) (-5.154) p-value of the joint significance

0.6874 0.041 0.0065 0.000 0.0000

Adjusted R-square 0.607 0.606 0.468 0.448 0.548 0.520 0.590 0.494 0.569 0.485 Observations 90 90 89 89 107 107 103 103 107 107

Robust t-statistics are in parentheses; *** p<0.01, ** p<0.05, * p<0.1. All regressions include a constant, initial per capita GDP (log), investment-GDP ratio, initial human capital, population growth, openness, political violence, share of government expenditure, ToT volatility, and dummies for regions, legal origins and landlocked countries. χ = Private credit/GDP and Polity2 are also controlled. Dummy-1: 1 = if BC volatility < 33% percentile in the sample; 0 = otherwise. Dummy-2: 1 = if BC volatility >= 33% percentile but < 67% percentile in the sample; 0 = otherwise. Dummy-3: 1 = if BC volatility >= 67% percentile in the sample; 0 = otherwise.

42

Table-4: OLS estimation using cross-sectional data (Developing (Low and medium income) countries)

Variables (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 1960-2007 1960-1980 1970-2007 1980-2007χ 1980-2007 BC volatility 0.054 0.086 0.023 0.114 0.024 -0.146 0.093 -0.206* 0.011 -0.218*** (0.604) (0.982) (0.137) (0.713) (0.324) (-1.650) (1.421) (-1.925) (0.178) (-3.204) LR volatility 0.129 0.330 -0.403*** -0.546*** -0.500*** (0.726) (1.103) (-3.499) (-5.873) (-4.750) p-value of the joint significance

0.555 0.460 0.000 0.000 0.000

Adjusted R-square 0.449 0.456 0.225 0.222 0.455 0.382 0.597 0.464 0.564 0.453 Observations 64 64 63 63 75 75 73 73 75 75

Robust t-statistics are in parentheses; *** p<0.01, ** p<0.05, * p<0.1. All regressions include a constant, initial per capita GDP (log), investment-GDP ratio, initial human capital, population growth, openness, political violence, share of government expenditure, ToT volatility, and dummies for regions, legal origins and landlocked countries. χ = Private credit/GDP and Polity2 are also controlled.

Table-5: OLS estimation using cross-sectional data: Disaggregating by the intensity of BC volatility (Developing (Low and medium income) countries)

Variables (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 1960-2007 1960-1980 1970-2007 1980-2007χ 1980-2007 BC volatility * Dummy-1

-0.003 0.056 0.499 0.634 0.281 0.052 0.145 -0.361 0.210 -0.064 (-0.010) (0.230) (0.731) (0.959) (1.015) (0.169) (0.348) (-0.687) (0.482) (-0.135)

BC volatility * Dummy-2

0.064 0.103 -0.177 -0.085 0.291 0.079 0.040 -0.412 -0.011 -0.332 (0.342) (0.627) (-0.413) (-0.207) (1.510) (0.407) (0.180) (-1.376) (-0.047) (-1.298)

BC volatility * Dummy-3

0.040 0.081 0.051 0.131 0.080 -0.105 0.094 -0.228 0.022 -0.211** (0.372) (0.845) (0.210) (0.591) (0.896) (-1.017) (1.224) (-1.651) (0.273) (-2.378)

LR volatility 0.141 0.260 -0.417*** -0.538*** -0.489*** (0.790) (0.920) (-3.495) (-4.880) p-value of the joint significance

0.789 0.0827 0.001 0.000 0.000

Adjusted R-square

0.427 0.433 0.293 0.297 0.462 0.380 0.584 0.456 0.556 0.450

Observations 64 64 63 63 75 75 73 73 75 75 Robust t-statistics are in parentheses; *** p<0.01, ** p<0.05, * p<0.1. All regressions include a constant, initial per capita GDP (log), investment-GDP ratio, initial human capital, population growth, openness, political violence, share of government expenditure, ToT volatility, and dummies for regions, legal origins and landlocked countries. χ = Private credit/GDP and Polity2 are also controlled. Dummy-1: 1 = if BC volatility < 33% percentile in the sample; 0 = otherwise. Dummy-2: 1 = if BC volatility >= 33% percentile but < 67% percentile in the sample; 0 = otherwise. Dummy-3: 1 = if BC volatility >= 67% percentile in the sample; 0 = otherwise.

43

Table-6: OLS estimation using cross-sectional data (Developed countries)

Variables (1) (2) (3) (4) (5) (6) (7) (8) 1960-2007 1960-1980 1970-2007 1980-2007 BC volatility 0.186 0.201 0.040 0.102 -0.071 0.028 -0.002 0.074 (1.229) (1.424) (0.402) (1.223) (-1.021) (0.455) (-0.038) (1.508) LR volatility 0.144 0.324 0.525*** 0.299** (0.456) (1.388) (3.475) (2.127) p-value of the joint significance

0.374 0.260 0.006 0.089

Adjusted R-square 0.811 0.823 0.799 0.800 0.890 0.856 0.791 0.786 Observations 30 30 28 28 38 38 38 38

Robust t-statistics are in parentheses; *** p<0.01, ** p<0.05, * p<0.1. All regressions include a constant, initial per capita GDP (log), investment-GDP ratio, initial human capital, openness, share of government expenditure, ToT volatility, private credit/GDP, Polity2 and dummies for regions, legal origins and landlocked countries.

Table-7: Pooled OLS estimation using 7-year panel data (all countries)

(1) (2) (3) (4) (5) (6) (7) (8) Panel A: 1960-2007 BC volatility 0.014 -0.111 -0.055 -0.193** (0.168) (-1.577) (-0.486) (-2.137) LR volatility -0.316** -0.248** (-2.244) (-2.229) Lagged BC volatility 0.022 0.033 0.009 0.001 (0.278) (0.636) (0.144) (0.016) Lagged LR volatility 0.027 -0.017 (0.184) (-0.238) p-value of the joint significance

0.018 0.000 0.796 0.971

Adjusted R-square 0.242 0.233 0.264 0.254 0.223 0.225 0.225 0.227 Observations 380 380 449 449 380 380 449 449 No. of countries 87 87 91 91 87 87 91 91 Panel B: 1978-2007 BC volatility 0.163 0.009 -0.061 -0.210** (0.954) (0.060) (-0.384) (-2.166) LR volatility -0.378** -0.259* (-2.220) (-1.733) Lagged BC volatility 0.058 0.078 0.143 0.057 (0.671) (1.000) (1.123) (0.923) Lagged LR volatility 0.051 -0.163 (0.275) (-1.033) p-value of the joint significance

0.090 0.000 0.607 0.533

Adjusted R-square 0.224 0.213 0.201 0.192 0.216 0.219 0.147 0.145 Observations 273 273 314 314 273 273 314 314 No. of countries 100 100 106 106 100 100 106 106

Robust clustered (at the country level) t-statistics are in parentheses; *** p<0.01, ** p<0.05, * p<0.1. All regressions include a constant, time dummies, lag of (initial per capita GDP (log), investment-GDP ratio, population growth, openness, political violence, share of government expenditure, ToT volatility), initial human capital for each interval, and dummies for regions, legal origins and landlocked countries. Columns (1), (2), (5) and (6) additionally control for private credit/GDP and polity2.

44

Table-8: Pooled OLS estimation using 7-year panel data (Developing (low and middle income) countries)

(1) (2) (3) (4) (5) (6) (7) (8) Panel A: 1960-2007 BC volatility 0.024 -0.146* -0.093 -0.215** (0.235) (-1.853) (-0.741) (-2.645) LR volatility -0.426** -0.212 (-2.366) (-1.516) Lagged BC volatility 0.061 0.033 0.006 -0.007 (0.596) (0.490) (0.071) (-0.139) Lagged LR volatility -0.074 -0.024 (-0.363) (-0.280) p-value of the joint significance

0.005 0.000 0.829 0.925

Adjusted R-square 0.221 0.206 0.238 0.232 0.189 0.192 0.193 0.196 Observations 262 262 324 324 262 262 324 324 No. of countries 63 63 66 66 63 63 66 66 Panel B: 1978-2007 BC volatility -0.017 -0.208* -0.210 -0.300*** (-0.123) (-1.764) (-1.601) (-4.099) LR volatility -0.469** -0.150 (-2.439) (-1.120) Lagged BC volatility 0.038 -0.006 0.139 0.035 (0.368) (-0.084) (0.863) (0.465) Lagged LR volatility -0.114 -0.190 (-0.531) (-1.040) p-value of the joint significance

0.003 0.000 0.866 0.489

Adjusted R-square 0.337 0.319 0.261 0.261 0.279 0.282 0.153 0.150 Observations 188 188 224 224 188 188 224 224 No. of countries 71 71 75 75 71 71 75 75

Robust clustered (at the country level) t-statistics are in parentheses; *** p<0.01, ** p<0.05, * p<0.1. All regressions include a constant, time dummies, lag of (initial per capita GDP (log), investment-GDP ratio, population growth, openness, political violence, share of government expenditure, ToT volatility), initial human capital for each interval, and dummies for regions, legal origins and landlocked countries. Columns (1), (2), (5) and (6) additionally control for private credit/GDP and polity2.

45

Table-9: Pooled OLS estimation using 7-year panel data (Developed countries)

(1) (2) (3) (4) Panel A: 1960-2007 BC volatility 0.035 -0.029 (0.248) (-0.271) LR volatility -0.177 (-0.990) Lagged BC volatility -0.084 -0.055 (-0.614) (-0.473) Lagged LR volatility 0.061 (0.429) p-value of the joint significance 0.541 0.822 Adjusted R-square 0.494 0.491 0.489 0.493 Observations 142 142 142 142 No. of countries 30 30 30 30 Panel B: 1978-2007 BC volatility 0.572** 0.622*** (2.663) (5.115) LR volatility 0.100 (0.300) Lagged BC volatility 0.069 0.284*** (0.457) (2.932) Lagged LR volatility 0.467* (1.733) p-value of the joint significance 0.000 0.011 Adjusted R-square 0.385 0.392 0.278 0.260 Observations 104 104 104 104 No. of countries 36 36 36 36

Robust clustered (at the country level) t-statistics are in parentheses; *** p<0.01, ** p<0.05, * p<0.1. All regressions include a constant, time dummies, lag of (initial per capita GDP (log), investment-GDP ratio, population growth, openness, share of government expenditure, ToT volatility, and private credit/GDP), initial human capital for each interval, and dummies for regions, legal origins and landlocked countries.

46

Table 10: Fixed effect estimation using the 7-year panel data (Angus Maddison historical data

for the 1875-2010 period)

(1) (2) (3) (4) Panel A: All countries BC volatility 0.029 -0.126** (0.209) (-2.296) LR volatility -0.300 (-1.276) Lagged BC volatility -0.080 0.166*** (-1.192) (4.727) Lagged LR volatility 0.480*** (4.061) p-value of the joint significance 0.014 0.000 Within R-square 0.276 0.265 0.318 0.290 Between R-square 0.017 0.020 0.011 0.007 Observations 504 504 476 476 No. of countries 28 28 28 28 Panel B: Developed countries BC volatility 0.134 -0.134** (0.981) (-2.264) LR volatility -0.507* (-2.085) Lagged BC volatility -0.115 0.185*** (-1.467) (6.406) Lagged LR volatility 0.580*** (4.008) p-value of the joint significance 0.010 0.000 Within R-square 0.391 0.361 0.427 0.389 Between R-square 0.424 0.427 0.324 0.328 Observations 360 360 340 340 No. of countries 20 20 20 20

Robust clustered (at the country level) t-statistics are in parentheses; *** p<0.01, ** p<0.05, * p<0.1. All regressions include a constant, initial log income for each 7-year interval, time dummies, and dummies for the pre-1914, 1914-1945, 1946-1985; and post-1985 periods. Countries in Panel A are: Argentina, Australia, Austria, Belgium, Brazil, Canada, Italy, Chile, Colombia, Denmark, Finland, France, Germany, Greece, Netherlands, Japan, Norway, New Zealand, Peru, Portugal, Spain, Sri Lanka, Sweden, Switzerland, UK, Uruguay, USA and Venezuela. Countries in Panel B are: Australia, Austria, Belgium, Canada, Italy, Denmark, Finland, France, Germany, Greece, Netherlands, Japan, Norway, New Zealand, Portugal, Spain, Sweden, Switzerland, UK and USA.

47

Table 11: Replication of Ramey and Ramey (1995) using PWT5.6 and PWT 8.0 data

(1) (2) (3) (4) Panel A: PWT 5.6 data for 92 Developing countries (1960-1985 period) Total volatility -0.154** (-2.610) [-2.337] BC volatility -0.161** -0.109 0.006 (-2.594) (-1.636) (0.066) LR volatility -0.363* (-1.720) Observations 92 92 92 92 Adjusted R-squared 0.047 0.042 0.209 0.233 Panel B: PWT 5.6 data for 24 OECD countries (1950-1988 period) Total volatility 0.147 (0.924) [0.672] BC volatility -0.119 -0.408** -0.417** (-0.574) (-2.463) (-2.508) LR volatility 0.200 (0.767) Observations 24 24 24 24 Adjusted R-squared -0.024 -0.038 0.759 0.751 Panel B: PWT 8.0 data for 24 OECD countries (1950-1988 period) Total volatility 0.364 (1.492) [1.986]* BC volatility 0.263 0.170 -0.193 (0.769) (0.834) (-1.245) LR volatility 0.816** (2.658) Observations 24 24 24 24 Adjusted R-squared 0.113 0.002 0.639 0.747

Robust t-statistics in parentheses; Non-robust t-statistics in bracket; *** p<0.01, ** p<0.05, * p<0.1. Notes: Columns (3)-(4) control for initial log GDP per capita, average population growth, average investment share of GDP and initial human capital.

48

Table-12: Relative contribution of BC volatility and persistence in volatility

(1) (2) (3) (4) (5) (6) Panel A (Cross-sectional correlation) PWT (1970-2007) PWT (1980-2007) BC volatility -0.002 -0.121* 0.053 -0.157* (-0.025) (-1.709) (1.045) (-1.724) LR volatility -0.292** -0.458*** (-2.195) (-5.776) Total volatility -0.132** -0.187*** (-2.048) (-2.848) Panel B (Panel correlation) PWT (1978-2007) (Developing countries) Angus Maddison (1875-2010) BC volatility -0.017 -0.208* 0.029 -0.126** (-0.123) (-1.764) (0.209) (-2.296) LR volatility -0.469** -0.300 (-2.439) (-1.276) Total volatility -0.188 (-1.897) -0.156 (-4.275) Panel C (Panel lagged effect) PWT (1978-2007) (Developed countries) Angus Maddison (1875-2010) Lagged BC volatility 0.069 0.284*** -0.080 0.166*** (0.457) (2.932) (-1.192) (4.727) Lagged LR volatility 0.467* 0.480*** (1.733) (4.061) Lagged total volatility 0.331 (4.087) 0.160 (4.516)

Robust clustered (at the country level) t-statistics are in parentheses; *** p<0.01, ** p<0.05, * p<0.1. Panel A: Columns (1), (2), (4) and (5) have been reproduced from columns (5), (6), (7) and (8), respectively, in Table 2. Panel B: Columns (1) and (2) have been reproduced from columns (1) and (2), respectively, in Table 8, Panel B. Columns (4) and (5) have been reproduced from columns (1) and (2), respectively, in Table 10, Panel A. Panel C: Columns (1) and (2) have been reproduced from columns (3) and (4), respectively, in Table 9, Panel B. Columns (4) and (5) have been reproduced from columns (5) and (6), respectively, in Table 10, Panel A.

49

Figures

Table 1: Comparison of long-run growth trajectories

(a) Namibia vs. Nepal

(b) Columbia vs. Australia

(c) Argentina vs. Burkina Faso

(d) Romania vs. Malaysia

(e) Japan vs. Cyprus

(f) Mauritania vs. Fiji

-.01

0.0

1.0

2.0

3.0

4Lo

ng-r

un g

row

th ra

te

1960 1970 1980 1990 2000Year

Colombia Australia

-.02

0.0

2.0

4.0

6Lo

ng-r

un g

row

th ra

te

1960 1970 1980 1990 2000Year

Namibia Nepal

-.04

-.02

0.0

2.0

4Lo

ng-r

un g

row

th ra

te

1960 1970 1980 1990 2000Year

Burkina Faso Argentina

-.1-.0

50

.05

.1Lo

ng-r

un g

row

th ra

te

1960 1970 1980 1990 2000Year

Romania Malaysia

0.0

5.1

.15

Long

-run

gro

wth

rate

1960 1970 1980 1990 2000Year

Japan Cyprus

-.05

0.0

5.1

.15

Long

-run

gro

wth

rate

1960 1970 1980 1990 2000Year

Mauritania Fiji

50

(g) Israel vs. Egypt

(h) Hong-Kong vs. Bangladesh

(i) Niger vs. Cyprus

(j) Japan vs. Austria

0.0

5.1

.15

Long

-run

gro

wth

rate

1960 1970 1980 1990 2000Year

Egypt Israel

-.05

0.0

5.1

Long

-run

gro

wth

rate

1960 1970 1980 1990 2000Year

Hong Kong Bangladesh

-.1-.0

50

.05

.1Lo

ng-r

un g

row

th ra

te

1960 1970 1980 1990 2000Year

Niger Cyprus

0.0

5.1

.15

Long

-run

gro

wth

rate

1960 1970 1980 1990 2000Year

Japan Austria

51

Figure 2: Relationship of initial per capita GDP (log) with BC and LR volatility

1. (a)

1. (b)

Figure 3: Relationship between BC and LR volatility

ARG

AUSAUT

BDI

BEL

BEN

BFA

BGD

BOL

BRA BRB

BWA

CAF

CAN CHE

CHL

CHN

CIVCMR

ZAR

COG

COL

COM

CPV

CRI

CYP

DEUDNK

DOM

ECUEGY

ESP

ETH

FIN

FJI

FRA

GBR

GHA

GIN

GMB

GRC

GTM

HKG

HNDIDN

IND

IRL

ISL

ISR

ITA

JAM

JOR

JPN

KEN

KOR

LKA

LSO

LUX

MARMDG

MEX

MLI

MLT

MOZ

MRT

MUS

MWI

MYS

NAM

NERNGA

NLDNOR

NPLNZL

PAK

PAN

PER

PHLPRTPRY

ROM

SEN

SGP

SLVSWE

TCD

TGO

THA

TTO

TUNTUR

TWNTZAUGA

URY

USA

VEN

ZAF

ZMB

ZWE

0.0

2.0

4.0

6.0

8B

usin

ess-

cycl

e vo

latil

ity

6 7 8 9 10Initial per capital GDP (log)

ARG

AUS

AUT

BDI

BELBENBFA

BGD

BOL

BRA BRB

BWA

CAF CANCHE

CHLCHN

CIV

CMR

ZARCOG

COL

COM

CPV

CRICYP

DEUDNK

DOM

ECU

EGYESP

ETH

FINFJI

FRA

GBR

GHA

GIN

GMB

GRC

GTM HKG

HND

IDN

IND

IRLISL

ISR

ITA

JAM

JOR

JPN

KEN

KOR

LKA

LSO

LUX

MAR

MDG MEXMLI

MLTMOZ

MRT

MUS

MWI

MYSNAM

NER

NGA

NLD

NORNPL

NZLPAK

PAN

PER

PHLPRT

PRY

ROM

SEN

SGP

SLV

SWE

TCD

TGO

THA

TTO

TUN

TURTWN

TZA

UGA

URY

USA

VEN

ZAF

ZMB

ZWE

.01

.02

.03

.04

.05

Long

-run

vol

atili

ty

6 7 8 9 10Initial per capital GDP (log)

ARG

AUS

AUT

BDI

BELBEN BFA

BGD

BOL

BRABRB

BWA

CAFCANCHE

CHLCHN

CIV

CMR

ZAR COG

COL

COM

CPV

CRICYP

DEUDNK

DOM

ECU

EGYESP

ETH

FIN FJI

FRA

GBR

GHA

GIN

GMB

GRC

GTM HKG

HND

IDN

IND

IRLISL

ISR

ITA

JAM

JOR

JPN

KEN

KOR

LKA

LSO

LUX

MAR

MDGMEX MLI

MLTMOZ

MRT

MUS

MWI

MYSNAM

NER

NGA

NLD

NORNPL

NZLPAK

PAN

PER

PHLPRT

PRY

ROM

SEN

SGP

SLV

SWE

TCD

TGO

THA

TTO

TUN

TURTWN

TZA

UGA

URY

USA

VEN

ZAF

ZMB

ZWE

.01

.02

.03

.04

.05

Long

-run

vol

atili

ty

0 .02 .04 .06 .08Business-cycle volatility

52

Appendix

A.1: Average growth, BC volatility and LR volatility for the 1960-2007 period

WB code

Country name Average growth

Standard deviation

Business-cycle volatility

Long-run volatility

High income countries AUS Australia 0.0211 0.0175 0.0141 0.0081 AUT Austria 0.0275 0.0177 0.0133 0.0109 BEL Belgium 0.0260 0.0183 0.0141 0.0108 CYP Cyprus 0.0430 0.0590 0.0556 0.0198 DEU Germany 0.0237 0.0184 0.0145 0.0096 DNK Denmark 0.0233 0.0210 0.0165 0.0099 ESP Spain 0.0324 0.0269 0.0130 0.0168 FRA France 0.0248 0.0176 0.0109 0.0128 GBR United Kingdom 0.0222 0.0194 0.0172 0.0077 IRL Ireland 0.0383 0.0272 0.0174 0.0196 ISR Israel 0.0342 0.0646 0.0531 0.0358 ITA Italy 0.0277 0.0249 0.0186 0.0149 JPN Japan 0.0426 0.0506 0.0331 0.0362 KOR Korea, Republic of 0.0597 0.0361 0.0300 0.0157 LUX Luxembourg 0.0310 0.0313 0.0267 0.0154 MLT Malta 0.0467 0.0435 0.0194 0.0329 NLD Netherlands 0.0244 0.0185 0.0134 0.0119 NOR Norway 0.0290 0.0156 0.0111 0.0087 PRT Portugal 0.0335 0.0328 0.0233 0.0201 SGP Singapore 0.0543 0.0388 0.0289 0.0233 TWN Taiwan 0.0572 0.0264 0.0218 0.0138 USA United States 0.0225 0.0194 0.0168 0.0075 HKG Hong Kong 0.0477 0.0418 0.0351 0.0198 CAN Canada 0.0221 0.0195 0.0151 0.0106 SWE Sweden 0.0228 0.0191 0.0138 0.0109 FIN Finland 0.0297 0.0281 0.0195 0.0164 GRC Greece 0.0328 0.0401 0.0242 0.0273 ISL Iceland 0.0287 0.0363 0.0260 0.0181 CHE Switzerland 0.0149 0.0222 0.0164 0.0116 NZL New Zealand 0.0144 0.0271 0.0236 0.0114

53

BRB Barbados 0.0224 0.0431 0.0255 0.0264 GNQ Equatorial Guinea 0.0654 0.1327 0.0909 0.0982 TTO Trinidad & Tobago 0.0278 0.0517 0.0254 0.0394 Upper middle income countries BWA Botswana 0.0639 0.0573 0.0465 0.0292 CHN China 0.0598 0.0585 0.0306 0.0264 MYS Malaysia 0.0412 0.0389 0.0332 0.0198 TUN Tunisia 0.0341 0.0445 0.0359 0.0231 THA Thailand 0.0497 0.0491 0.0413 0.0257 COL Colombia 0.0196 0.0219 0.0150 0.0125 DOM Dominican Republic 0.0289 0.0507 0.0393 0.0220 PAN Panama 0.0316 0.0442 0.0331 0.0222 TUR Turkey 0.0263 0.0378 0.0334 0.0138 CRI Costa Rica 0.0218 0.0338 0.0240 0.0181 MEX Mexico 0.0196 0.0331 0.0266 0.0171 BRA Brazil 0.0260 0.0385 0.0247 0.0259 MUS Mauritius 0.0305 0.0523 0.0424 0.0282 ROM Romania 0.0411 0.0553 0.0259 0.0443 CHL Chile 0.0242 0.0520 0.0410 0.0281 ECU Ecuador 0.0195 0.0420 0.0341 0.0248 URY Uruguay 0.0132 0.0415 0.0302 0.0197 NAM Namibia 0.0124 0.0357 0.0247 0.0186 PER Peru 0.0103 0.0512 0.0384 0.0249 ARG Argentina 0.0114 0.0528 0.0433 0.0216 IRN Iran 0.0107 0.1058 0.0946 0.0419 ZAF South Africa 0.0101 0.0251 0.0165 0.0155 JAM Jamaica 0.0069 0.0378 0.0267 0.0239 JOR Jordan 0.0113 0.0676 0.0446 0.0437 VEN Venezuela 0.0071 0.0546 0.0462 0.0220 GAB Gabon 0.0198 0.1032 0.0794 0.0576 Lower middle income countries EGY Egypt 0.0370 0.0374 0.0322 0.0154 LKA Sri Lanka 0.0338 0.0236 0.0164 0.0093 MAR Morocco 0.0265 0.0501 0.0403 0.0118

54

PAK Pakistan 0.0260 0.0207 0.0172 0.0106 IND India 0.0292 0.0335 0.0275 0.0143 LSO Lesotho 0.0266 0.0661 0.0621 0.0217 FJI Fiji 0.0185 0.0454 0.0425 0.0169 HND Honduras 0.0106 0.0314 0.0257 0.0130 IDN Indonesia 0.0329 0.0397 0.0296 0.0215 CPV Cape Verde 0.0298 0.0620 0.0385 0.0294 GTM Guatemala 0.0147 0.0245 0.0125 0.0192 PHL Philippines 0.0133 0.0307 0.0207 0.0187 SLV El Salvador 0.0142 0.0356 0.0178 0.0259 PRY Paraguay 0.0159 0.0363 0.0217 0.0258 SYR Syria 0.0211 0.0911 0.0769 0.0294 BOL Bolivia 0.0047 0.0387 0.0299 0.0218 CMR Cameroon 0.0054 0.0539 0.0434 0.0338 GHA Ghana 0.0037 0.0431 0.0352 0.0229 COG Congo, Republic of 0.0167 0.0640 0.0380 0.0393 NGA Nigeria 0.0034 0.0777 0.0586 0.0432 CIV Cote d`Ivoire 0.0022 0.0532 0.0401 0.0290 SEN Senegal -0.0016 0.0431 0.0429 0.0126 ZMB Zambia -0.0038 0.0490 0.0372 0.0286 Low income countries NPL Nepal 0.0129 0.0276 0.0277 0.0097 BFA Burkina Faso 0.0115 0.0507 0.0440 0.0139 MLI Mali 0.0123 0.0550 0.0516 0.0165 BEN Benin 0.0109 0.0347 0.0303 0.0130 TZA Tanzania 0.0140 0.0351 0.0239 0.0189 MOZ Mozambique 0.0177 0.0515 0.0390 0.0313 BGD Bangladesh 0.0112 0.0415 0.0353 0.0187 TCD Chad 0.0066 0.0831 0.0669 0.0382 BDI Burundi 0.0037 0.0593 0.0468 0.0255 GIN Guinea 0.0030 0.0346 0.0282 0.0176 UGA Uganda 0.0097 0.0458 0.0281 0.0335 KEN Kenya 0.0054 0.0307 0.0234 0.0116 MWI Malawi 0.0163 0.0724 0.0601 0.0330 RWA Rwanda 0.0056 0.1162 0.1143 0.0297

55

ETH Ethiopia 0.0065 0.0692 0.0638 0.0224 MRT Mauritania 0.0183 0.0827 0.0641 0.0393 COM Comoros 0.0076 0.0376 0.0271 0.0182 ZWE Zimbabwe -0.0035 0.0674 0.0562 0.0328 GMB Gambia, The -0.0020 0.0382 0.0343 0.0102 GNB Guinea-Bissau -0.0094 0.0858 0.0827 0.0242 TGO Togo 0.0020 0.0591 0.0469 0.0297 NER Niger -0.0120 0.0614 0.0542 0.0250 CAF Central African

Republic -0.0103 0.0387 0.0354 0.0115

MDG Madagascar -0.0081 0.0451 0.0398 0.0174 ZAR Congo, Dem. Rep. -0.0277 0.0607 0.0332 0.0392

Note: BC volatility and LR volatility are calculated as the standard deviation of the Baxter-King (1999) band- and low-pass filtered series with a window of 3 years and critical periodicity of 2-8 years.

56

A.2: OLS estimation using cross-sectional data (all countries): Alternative filter weights for developing countries)

Variables (1) (2) (3) (4) (5) (6) (7) (8) Panel A: All countries 1960-2007 1960-1980 1970-2007 1980-2007 BC volatility 0.026 0.068 -0.075 0.088 0.024 -0.125 0.057 -0.177** (0.261) (0.913) (-0.513) (0.645) (0.323) (-1.620) (1.003) (-2.561) LR volatility 0.094 0.354 -0.240** -0.359*** (0.650) (1.514) (-2.373) (-6.456) p-value of the joint significance

0.548 0.303 0.007 0.000

Adjusted R-square 0.613 0.615 0.440 0.415 0.544 0.509 0.578 0.484 Observations 90 90 89 89 107 107 107 107 Panel B: Developing countries BC volatility 0.039 0.088 -0.189 0.079 0.051 -0.156 0.056 -0.237*** (0.340) (0.911) (-0.905) (0.489) (0.541) (-1.588) (0.692) (-2.994) LR volatility 0.100 0.507 -0.307*** -0.385*** (0.612) (1.535) (-2.945) (-4.947) p-value of the joint significance

0.619 0.308 0.001 0.000

Adjusted R-square 0.447 0.455 0.258 0.214 0.446 0.379 0.549 0.442 Observations 64 64 63 63 75 75 75 75

Robust t-statistics are in parentheses; *** p<0.01, ** p<0.05, * p<0.1. All regressions include a constant, initial per capita GDP (log), investment-GDP ratio, initial human capital, population growth, openness, political violence, share of government expenditure, ToT volatility, and dummies for regions, legal origins and landlocked countries.

57

A.3: OLS estimation using cross-sectional data (all countries): Hodrick-Prescott filter

Variables (1) (2) (3) (4) (5) (6) (7) (8) 1960-2007 1960-2008 1970-2007 1980-2007 BC volatility 0.020 0.079 0.016 0.155 -0.054 -0.137* -0.009 -0.206*** (0.244) (1.067) (0.105) (0.951) (-0.700) (-1.721) (-0.131) (-2.886) LR volatility 0.203 0.397 -0.204 -0.452*** (1.285) (1.514) (-1.105) (-3.914) p-value of the joint significance

0.287 0.273 0.089 0.000

Adjusted R-square 0.620 0.617 0.447 0.425 0.521 0.512 0.559 0.496 Observations 90 90 89 89 107 107 107 107

Robust t-statistics in parentheses; *** p<0.01, ** p<0.05, * p<0.1. All regressions include a constant, initial per capita GDP (log), investment-GDP ratio, initial human capital, population growth, openness, political violence, share of government expenditure, ToT volatility, and dummies for regions, legal origins and landlocked countries. A.4: OLS estimation using cross-sectional data (all countries): Christiano-Fitzgerald filter

Variables (1) (2) (3) (4) (5) (6) (7) (8) 1960-2007 1960-1980 1970-2007 1980-2007 BC volatility 0.031 0.073 0.021 0.123 -0.008 -0.119* 0.009 -0.171*** (0.438) (1.057) (0.138) (0.850) (-0.114) (-1.684) (0.158) (-2.873) LR volatility 0.126 0.329* -0.229** -0.372*** (1.157) (1.688) (-2.017) (-4.720) p-value of the joint significance

0.343 0.157 0.013 0.000

Adjusted R-square 0.618 0.617 0.440 0.423 0.539 0.511 0.577 0.496 Observations 90 90 89 89 107 107 107 107

Robust t-statistics in parentheses; *** p<0.01, ** p<0.05, * p<0.1. All regressions include a constant, initial per capita GDP (log), investment-GDP ratio, initial human capital, population growth, openness, political violence, share of government expenditure, ToT volatility, and dummies for regions, legal origins and landlocked countries.

58

A.5: Comparison of spectral densities

The spectral density for averaging over T years is given by:

( ) ( ) ( )21/ 1 cos / 1 cosT Tω ω− − , where ω is the frequency ranging between 0 and π (for

derivation, see Sargent, 1987, p. 275). The spectral densities for T = 5, 7, 8 and 10 are displayed

in Appendix Figure A.1. They are normalized using appropriate scalars so that the area under the

curves are equal. A vertical line is drawn at 0.786 to mark the critical frequency that separates

the long-run from cyclical components. Note that the periodicity (p) and frequency are inversely

related by the formula: 2 /p π ω= . For a critical periodicity of 8 years, the corresponding critical

frequency is 0.786. It can be seen from the graph that 5-year averaging does not reweight the

variances of the raw series enough across low frequencies, thus the transformed data are more

likely to be contaminated by high frequencies. The area under the spectral density to the right of

the vertical line is 14% of the total area for 5-year averaging. The area substantially reduces

9.3% for 7-year averaging; it remains the same for 8-year averaging and reduces only to 8.8% for

10-year averaging.

Figure A.1: Spectral density for 5-, 7-, 8- and 10-year averaging.

02

46

810

Spe

ctra

l den

sity

0 1 2 3.786Frequency

5-year average 7-year average8-year average 10-year average

59